论文标题
在加权贪婪型基础上
On Weighted Greedy-type Bases
论文作者
论文摘要
在本文中，我们研究了阈值贪婪算法（TGA）的权重。虽然先前的工作集中在每个正整数上的顺序权重$ς=（s_n）_ {n \ in \ mathbb {n}} $上我们定义并描述了$ω$ - （几乎）贪婪的基础。此外，我们利用现有的结果表明存在$ω$的无条件基础，该基础不是$ς$ - 对于任何重量序列$ς$而言，几乎是贪婪。最后但并非最不重要的一点是，我们显示了$ω$ -Semi-Greedy bases和$ω$之间的等效性 - 几乎是贪婪的基础时，当$ω$是所谓的结构化重量时，因此很大程度上扩展了以前已知的等价性，该等价性持有序列权重。
In this paper, we study weights for the Thresholding Greedy Algorithm (TGA). While previous work focused on sequential weights $ς= (s_n)_{n\in\mathbb{N}}$ on each positive integer, we study a more general weight $ω= (w_A)_{A\subset\mathbb{N}}$ on each set $A\subset \mathbb{N}$. We define and characterize $ω$-(almost) greedy bases. Furthermore, we leverage existing results to show that there exists an $ω$-greedy unconditional basis that is not $ς$-almost greedy for any weight sequence $ς$. Last but not least, we show the equivalence between $ω$-semi-greedy bases and $ω$-almost greedy bases when $ω$ is a so-called structured weight, thus considerably extending the equivalence previously known to hold for sequential weights.
